Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Effects of convection on the removal of the multiplicity of stable states in one-dimensional vertical models

Here I develop a model of a radiative-convective atmosphere with both radiative and convective schemes highly simplified. The atmospheric absorption of radiation at selective wavelengths makes use of constant mass absorption coefficients in finite width spectral bands. The convective regime is introduced by using a prescribed lapse rate in the troposphere. The main novelty of the radiative-convective model developed here is that it is solved without using any angular approximation for the radiation field. The solution obtained in the purely radiation mode (i. e. with convection ignored) leads to multiple equilibria of stable states, being very similar to some results recently found in simple models of planetary atmospheres. However, the introduction of convective processes removes the multiple equilibria of stable states. This shows the importance of taking convective processes into account even for qualitative analyses of planetary atmosphere

Effects of riparian vegetation removal on nutrient retention in a Mediterranean stream

We examined the effects of riparian vegetation removal on algal dynamics and stream nutrient retention efficiency by comparing NH4-N and PO4-P uptake lengths from a logged and an unlogged reach in Riera Major, a forested Mediterranean stream in northeastern Spain. From June to September 1995, we executed 6 short-term additions of N (as NH4Cl) and P (as Na2HPO4) in a 200-m section to measure nutrient uptake lengths. The study site included 2 clearly differentiated reaches in terms of canopy cover by riparian trees: the first 100 m were completely logged (i.e., the logged reach) and the remaining 100 m were left intact (i.e., the shaded reach). Trees were removed from the banks of the logged reach in the winter previous to our sampling. In the shaded reach, riparian vegetation was dominated by alders (Alnus glutinosa). The study was conducted during summer and fall months when differences in light availability between the 2 reaches were greatest because of forest canopy conditions. Algal biomass and % of stream surface covered by algae were higher in the logged than in the shaded reach, indicating that logging had a stimulatory effect on algae in the stream. Overall, nutrient retention efficiency was higher (i.e., shorter uptake lengths) in the logged than in the shaded reach, especially for PO4-P. Despite a greater increase in PO4-P retention efficiency relative to that of NH4-N following logging, retention efficiency for NH4-N was higher than for PO4-P in both study reaches. The PO4-P mass-transfer coefficient was correlated with primary production in both study reaches, indicating that algal activity plays an important role in controlling PO4-P dynamics in this stream. In contrast, the NH4-N mass-transfer coefficient showed a positive relation-ship only with % of algal coverage in the logged reach, and was not correlated with any algal-related parameter in the shaded reach. The lack of correlation with algal production suggests that mechanisms other than algal activity (i.e., microbial heterotrophic processes or abiotic mechanisms) may also influence NH4-N retention in this stream. Overall, this study shows that logging disturbances in small shaded streams may alter in-stream ecological features that lead to changes in stream nutrient retention efficiency. Moreover, it emphasizes that alteration of the tight linkage between the stream channel and the adjacent riparian zone may directly and indirectly impact biogeochemical processes with implications for stream ecosystem functioning.

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant mass absorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analytically solved by a discrete ordinate method. The general solution is analyzed for a water vapor saturated atmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stable equilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing from previous radiative–convective models, we find that the amount of carbon dioxide strongly modifies the value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption of radiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect of carbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runaway greenhouse state than thin carbon dioxide ones

Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Efficient energy transfer from Si clusters to Er3+ in complex silicate glasses

We present an extensive study of the structural and optical emission properties in aluminum silicates and soda-lime silicates codoped with Si nanoclusters (Si-nc) and Er. Si excess of 5 and 15¿at.¿% and Er concentrations ranging from 2×1019 up to 6×1020¿cm¿3 were introduced by ion implantation. Thermal treatments at different temperatures were carried out before and after Er implantation. Structural characterization of the resulting structures was performed to obtain the layer composition and the size distribution of Si clusters. A comprehensive study has been carried out of the light emission as a function of the matrix characteristics, Si and Er contents, excitation wavelength, and power. Er emission at 1540¿nm has been detected in all coimplanted glasses, with similar intensities. We estimated lifetimes ranging from 2.5¿to¿12¿ms (depending on the Er dose and Si excess) and an effective excitation cross section of about 1×10¿17¿cm2 at low fluxes that decreases at high pump power. By quantifying the amount of Er ions excited through Si-nc we find a fraction of 10% of the total Er concentration. Upconversion coefficients of about 3×10¿18¿cm¿3¿s¿1 have been found for soda-lime glasses and one order of magnitude lower in aluminum silicates.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.